Balanced cross correlation was previously implemented for optical pulses with different center wavelengths [see T. R. Schibli, et al., Opt. Lett. 28, 947 (2003)]. Using group delay dispersion (GDD) to vary the group delay between two pulses of different center frequency, this balanced cross-correlator was used to lock two independently mode-locked lasers with different optical spectra within 300 attoseconds residual timing jitter. Recently, it has also been shown that this method enables long-term (i.e., for a period greater than 12 hours) sub-femtosecond timing synchronization (see J. Kim, et al., “An Integrated Femtosecond Timing Distribution System for XFELs,” European Particle Accelerator Conference 2006). However, this method is limited to the case of optical pulses with different center wavelengths because the delay between the two pulses was generated by the group delay dispersion and because the balanced optical cross correlator used two nonlinear media. This method is not applicable to the case in which the two optical pulses have the same center wavelength.
In this case and in general, one can use fast photodiodes followed by a microwave mixer to extract the timing information, but the resolution and stability of this method are very limited due to the limited resolution and drifts of microwave mixers. Applicants believe that, thus far and beyond the methods described herein, no pure electronic method has achieved long-term (i.e., greater than 12-hour) stable sub-100 femtosecond resolution in the timing detection between two optical pulses.